Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
774 conjugacy classes of subgroups; only the 204 normal subgroups are shown.
This group has 774 conjugacy classes of subgroups — too many to draw. Only its 204 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#11745348 | C2 | semidirect |
| 2. #14272137 | C2 | semidirect |
| 3. #14272134 | C2 | semidirect |
| 4. D29⋊(C22⋊C8) | C2 | semidirect |
| 15. C2×#90796 | C22 | semidirect |
| 16. C2×D29⋊C8 | C22 | semidirect |
| 17. C22⋊#6599 | C22 | semidirect |
| 18. C22⋊#6599 | C22 | semidirect |
| 78. C2×D29 | #131 | semidirect |
| 109. C29 | #2880 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745348 | 2 |
| #14272137 | 2 |
| #14272134 | 2 |
| D29⋊(C22⋊C8) | 2 |
| C2×#41×D29 | 2 |
| #2880 | 29 |